document.write( "Question 575365: The perimeter of a rose garden is 140m and the area is 1200m squared. find the length and width of the garden. \n" ); document.write( "

Algebra.Com's Answer #369465 by josmiceli(19441) $\"\"$ $\"About$

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$\"+P+=+2W+%2B+2L+\"$
\n" ); document.write( " $\"+A+=+W%2AL+\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"+P+=+140+\"$ m
\n" ); document.write( " $\"+A+=+1200+\"$ m2
\n" ); document.write( "---------------
\n" ); document.write( "(1) $\"+140+=+2W+%2B+2L+\"$
\n" ); document.write( "(2) $\"+1200+=+W%2AL+\"$
\n" ); document.write( "------------------
\n" ); document.write( "(2) $\"+W+=+1200%2FL+\"$
\n" ); document.write( "Substitute (2) into (1)
\n" ); document.write( "(1) $\"+140+=+2%2A%28+1200%2FL+%29+%2B+2L+\"$
\n" ); document.write( "Multiply both sides by $\"+L+\"$
\n" ); document.write( "(1) $\"+140L+=+2400+%2B+2L%5E2+\"$
\n" ); document.write( "(1) $\"+2L%5E2+-+140L+%2B+2400+\"$
\n" ); document.write( "(1) $\"+L%5E2+-+70L+%2B+1200+\"$
\n" ); document.write( "Use quadratic equation
\n" ); document.write( " $\"L+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+1+\"$
\n" ); document.write( " $\"+b+=+-70+\"$
\n" ); document.write( " $\"+c+=+1200+\"$
\n" ); document.write( " $\"L+=+%28-%28-70%29+%2B-+sqrt%28+%28-70%29%5E2-4%2A1%2A1200+%29%29%2F%282%2A1%29+\"$
\n" ); document.write( " $\"L+=+%28+70+%2B-+sqrt%28+4900+-+4800+%29%29+%2F+2+\"$
\n" ); document.write( " $\"L+=+%28+70+%2B-+sqrt%28+100++%29%29+%2F+2+\"$
\n" ); document.write( " $\"+L+=+%28+70+%2B+10+%29+%2F+2+\"$
\n" ); document.write( " $\"+L+=+40+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+W+=+1200%2FL+\"$
\n" ); document.write( "(2) $\"+W+=+1200%2F40+\"$
\n" ); document.write( "(2) $\"+W+=+30+\"$
\n" ); document.write( "The length is 40 m
\n" ); document.write( "The width is 30 m \n" ); document.write( "

\n" );